cf111 was, as I understand it, referring to a delay during the return leg of a journey where it is not possible to abandon the journey (foremost, because one cannot alight the train). I made the point that the act of being transported to the destination (or origin of the overall journey - however you choose to describe it), though delayed, is not a service of 'zero value'.
In your example of being transported to Edinburgh on the Monday, surely you wanted to be in Edinburgh for the appointment 'first thing' on the Tuesday? In which case the transportation on the Monday, though delayed, still had some value, and compensation to the value of 100% of the single journey (or 200% of the single journey if a return ticket was held) - particularly in the case of high value long-distance fares (e.g. a £200 1st Advance) - seems disproportionate.